Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Transforming representations of movement from body- to world-centric space

Nature volume 601, pages 98–104 (2022)Cite this article

Subjects

Abstract

When an animal moves through the world, its brain receives a stream of information about the body’s translational velocity from motor commands and sensory feedback signals. These incoming signals are referenced to the body, but ultimately, they must be transformed into world-centric coordinates for navigation1,2. Here we show that this computation occurs in the fan-shaped body in the brain of Drosophila melanogaster. We identify two cell types, PFNd and PFNv3,4,5, that conjunctively encode translational velocity and heading as a fly walks. In these cells, velocity signals are acquired from locomotor brain regions6 and are multiplied with heading signals from the compass system. PFNd neurons prefer forward–ipsilateral movement, whereas PFNv neurons prefer backward–contralateral movement, and perturbing PFNd neurons disrupts idiothetic path integration in walking flies7. Downstream, PFNd and PFNv neurons converge onto hΔB neurons, with a connectivity pattern that pools together heading and translation direction combinations corresponding to the same movement in world-centric space. This network motif effectively performs a rotation of the brain’s representation of body-centric translational velocity according to the current heading direction. Consistent with our predictions, we observe that hΔB neurons form a representation of translational velocity in world-centric coordinates. By integrating this representation over time, it should be possible for the brain to form a working memory of the path travelled through the environment8,9,10.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: PFN neurons that encode heading and translational velocity.
Fig. 2: Velocity tuning in PFNd neurons from graded release of inhibition.
Fig. 3: Behaviour and connections downstream from PFN neurons.
Fig. 4: From heading and body-centric velocity to world-centric velocity.

Similar content being viewed by others

Data availability

The datasets generated and/or analysed during the current study are available from the corresponding author on reasonable request.

Code availability

Code for implementing the computational model is available at https://github.com/druckmann-lab/Translational-velocity-and-heading-model.

References

  1. Bicanski, A. & Burgess, N. Neuronal vector coding in spatial cognition. Nat. Rev. Neurosci. 21, 453–470 (2020).

    Article  CAS  PubMed  Google Scholar 

  2. Wang, C., Chen, X. & Knierim, J. J. Egocentric and allocentric representations of space in the rodent brain. Curr. Opin. Neurobiol. 60, 12–20 (2020).

    Article  CAS  PubMed  Google Scholar 

  3. Wolff, T., Iyer, N. A. & Rubin, G. M. Neuroarchitecture and neuroanatomy of the Drosophila central complex: A GAL4-based dissection of protocerebral bridge neurons and circuits. J. Comp. Neurol. 523, 997–1037 (2015).

    Article  PubMed  Google Scholar 

  4. Wolff, T. & Rubin, G. M. Neuroarchitecture of the Drosophila central complex: a catalog of nodulus and asymmetrical body neurons and a revision of the protocerebral bridge catalog. J. Comp. Neurol. 526, 2585–2611 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  5. Hulse, B. K. et al. A connectome of the Drosophila central complex reveals network motifs suitable for flexible navigation and context-dependent action selection. eLife 10, e66039 (2021).

    Article  PubMed  Google Scholar 

  6. Namiki, S., Dickinson, M. H., Wong, A. M., Korff, W. & Card, G. M. The functional organization of descending sensory-motor pathways in Drosophila. eLife 7, e34272 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  7. Behbahani, A. H., Palmer, E. H., Corfas, R. A. & Dickinson, M. H. Drosophila re-zero their path integrator at the center of a fictive food patch. Curr. Biol. 31, 4534–4546.e5 (2021).

    Article  CAS  PubMed  Google Scholar 

  8. Kim, I. S. & Dickinson, M. H. Idiothetic path integration in the fruit fly Drosophila melanogaster. Curr. Biol. 27, 2227–2238 e3 (2017).

    Article  CAS  PubMed  Google Scholar 

  9. Müller, M. & Wehner, R. Path integration in desert ants, Cataglyphis fortis. Proc. Natl Acad. Sci. USA 85, 5287–5290 (1988).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  10. Esch, H. & Burns, J. Distance estimation by foraging honeybees. J. Exp. Biol. 199, 155–162 (1996).

    Article  CAS  PubMed  Google Scholar 

  11. Ronacher, B. Path integration as the basic navigation mechanism of the desert ant Cataglyphis fortis (Forel, 1902) (Hymenoptera: Formicidae). Myrmecol. News 11, 53–62 (2008).

    Google Scholar 

  12. Corfas, R. A., Sharma, T. & Dickinson, M. H. Diverse food-sensing neurons trigger idiothetic local search in Drosophila. Curr. Biol. 29, 1660–1668.e4 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  13. Ronacher, B. D. & Wehner, R. Desert ants Cataglyphis fortis use self-induced optic flow to measure distance travelled. J. Comp. Physiol. A 177, 21–27 (1995).

    Article  Google Scholar 

  14. Schöne, H. Optokinetic speed control and estimation of travel distance in walking honeybees. J. Comp. Physiol. A 179, 587–592 (1996).

    ADS  Google Scholar 

  15. Wittlinger, M., Wehner, R. & Wolf, H. The ant odometer: stepping on stilts and stumps. Science 312, 1965–1967 (2006).

    Article  ADS  CAS  PubMed  Google Scholar 

  16. Tuthill, J. C. & Wilson, R. I. Mechanosensation and adaptive motor control in insects. Curr. Biol. 26, R1022–R1038 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  17. Seelig, J. D. & Jayaraman, V. Neural dynamics for landmark orientation and angular path integration. Nature 521, 186–191 (2015).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  18. Turner-Evans, D. et al. Angular velocity integration in a fly heading circuit. eLife 6, e23496 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

  19. Green, J. et al. A neural circuit architecture for angular integration in Drosophila. Nature 546, 101–106 (2017).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  20. Stone, T. et al. An anatomically constrained model for path integration in the bee brain. Curr. Biol. 27, 3069–3085.e11 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Shiozaki, H. M., Ohta, K. & Kazama, H. A multi-regional network encoding heading and steering maneuvers in Drosophila. Neuron 106, 126–141.e5 (2020).

    Article  CAS  PubMed  Google Scholar 

  22. Dana, H. et al. High-performance calcium sensors for imaging activity in neuronal populations and microcompartments. Nat. Methods 16, 649–657 (2019).

    Article  CAS  PubMed  Google Scholar 

  23. Reiser, M. B. & Dickinson, M. H. A modular display system for insect behavioral neuroscience. J. Neurosci. Methods 167, 127–139 (2008).

    Article  PubMed  Google Scholar 

  24. Scheffer, L. K. et al. A connectome and analysis of the adult Drosophila central brain. eLife 9, e57443 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Zheng, Z. et al. A complete electron microscopy volume of the brain of adult Drosophila melanogaster. Cell 174, 730–743 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  26. Eckstein, N. et al. Neurotransmitter classification from electron microscopy images at synaptic sites in Drosophila. Preprint at https://doi.org/10.1101/2020.06.12.148775 (2020).

  27. Liu, W. W. & Wilson, R. I. Glutamate is an inhibitory neurotransmitter in the Drosophila olfactory system. Proc. Natl Acad. Sci. USA 110, 10294–10299 (2013).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  28. Lacin, H. et al. Neurotransmitter identity is acquired in a lineage-restricted manner in the Drosophila CNS. eLife 8, e43701 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  29. Hampel, S., Franconville, R., Simpson, J. H. & Seeds, A. M. A neural command circuit for grooming movement control. eLife 4, e08758 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  30. DeAngelis, B. D., Zavatone-Veth, J. A. & Clark, D. A. The manifold structure of limb coordination in walking Drosophila. eLife 8, e46409 (2019).

    Article  PubMed  PubMed Central  Google Scholar 

  31. Rayshubskiy, A. et al. Neural circuit mechanisms for steering control in walking Drosophila. Preprint at https://doi.org/10.1101/2020.04.04.024703 (2020).

  32. Wittmann, T. & Schwegler, H. Path integration—a network model. Biol. Cybern. 73, 569–575 (1995).

    Article  MATH  Google Scholar 

  33. Homberg, U., Heinze, S., Pfeiffer, K., Kinoshita, M. & el Jundi, B. Central neural coding of sky polarization in insects. Philos. Trans. R. Soc. Lond. B 366, 680–687 (2011).

    Article  Google Scholar 

  34. Vinepinsky, E. et al. Representation of edges, head direction, and swimming kinematics in the brain of freely-navigating fish. Sci. Rep. 10, 14762 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  35. Wang, C. et al. Egocentric coding of external items in the lateral entorhinal cortex. Science 362, 945–949 (2018).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  36. Solstad, T., Boccara, C. N., Kropff, E., Moser, M.-B. & Moser, E. I. Representation of geometric borders in the entorhinal cortex. Science 322, 1865–1868 (2008).

    Article  ADS  CAS  PubMed  Google Scholar 

  37. Savelli, F., Yoganarasimha, D. & Knierim, J. J. Influence of boundary removal on the spatial representations of the medial entorhinal cortex. Hippocampus 18, 1270–1282 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  38. Deshmukh, S. S. & Knierim, J. J. Influence of local objects on hippocampal representations: landmark vectors and memory. Hippocampus 23, 253–267 (2013).

    Article  PubMed  Google Scholar 

  39. Byrne, P., Becker, S. & Burgess, N. Remembering the past and imagining the future: a neural model of spatial memory and imagery. Psychol. Rev. 114, 340–375 (2007).

    Article  PubMed  PubMed Central  Google Scholar 

  40. Bicanski, A. & Burgess, N. A neural-level model of spatial memory and imagery. eLife 7, e33752 (2018).

    Article  PubMed  PubMed Central  Google Scholar 

  41. Lyu, C., Abbott, L. F. & Maimon, G. Building an allocentric travelling direction signal via vector computation. Nature https://doi.org/10.1038/s41586-021-04067-0 (2021).

  42. Srinivasan, M., Zhang, S., Lehrer, M. & Collett, T. Honeybee navigation en route to the goal: visual flight control and odometry. J. Exp. Biol. 199, 237–244 (1996).

    Article  CAS  PubMed  Google Scholar 

  43. Wilson, R. I. & Laurent, G. Role of GABAergic inhibition in shaping odor-evoked spatiotemporal patterns in the Drosophila antennal lobe. J. Neurosci. 25, 9069–9079 (2005).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Pfeiffer, B. et al. Refinement of tools for targeted gene expression in Drosophila. Genetics 186, 735–755 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  45. Tirian, L. & Dickson, B. J. The VT GAL4, LexA, and split-GAL4 driver line collections for targeted expression in the Drosophila nervous system. Preprint at https://doi.org/10.1101/198648 (2017).

  46. Nern, A., Pfeiffer, B. D. & Rubin, G. M. Optimized tools for multicolor stochastic labeling reveal diverse stereotyped cell arrangements in the fly visual system. Proc. Natl Acad. Sci. USA 112, E2967–E2976 (2015).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  47. Miyamoto, T., Slone, J., Song, X. & Amrein, H. A fructose receptor functions as a nutrient sensor in the Drosophila brain. Cell 151, 1113–1125 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  48. Klapoetke, N. C. et al. Independent optical excitation of distinct neural populations. Nat. Methods 11, 338–346 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  49. Pfeiffer, B. D., Truman, J. W. & Rubin, G. M. Using translational enhancers to increase transgene expression in Drosophila. Proc. Natl Acad. Sci. USA 109, 6626–6631 (2012).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  50. von Reyn, C. R. et al. A spike-timing mechanism for action selection. Nat. Neurosci. 17, 962 (2014).

    Article  CAS  Google Scholar 

  51. Pologruto, T. A., Sabatini, B. L. & Svoboda, K. ScanImage: flexible software for operating laser scanning microscopes. Biomed. Eng. Online 2, 13 (2003).

    Article  PubMed  PubMed Central  Google Scholar 

  52. Gouwens, N. W. & Wilson, R. I. Signal propagation in Drosophila central neurons. J. Neurosci. 29, 6239–6249 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  53. Moore, R. J. et al. FicTrac: a visual method for tracking spherical motion and generating fictive animal paths. J. Neurosci. Methods 225, 106–119 (2014).

    Article  PubMed  Google Scholar 

  54. Morimoto, M. M. et al. Spatial readout of visual looming in the central brain of Drosophila. eLife 9, e57685 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  55. Pnevmatikakis, E. A. & Giovannucci, A. NoRMCorre: An online algorithm for piecewise rigid motion correction of calcium imaging data. J. Neurosci. Methods 291, 83–94 (2017).

    Article  CAS  PubMed  Google Scholar 

  56. Kempter, R., Leibold, C., Buzsáki, G., Diba, K. & Schmidt, R. Quantifying circular–linear associations: hippocampal phase precession. J. Neurosci. Methods 207, 113–124 (2012).

    Article  PubMed  Google Scholar 

  57. Clements, J. et al. neuPrint: Analysis Tools for EM Connectomics. Preprint at https://doi.org/10.1101/2020.01.16.909465 (2020).

  58. Bates, A. S. et al. The natverse, a versatile toolbox for combining and analysing neuroanatomical data. eLife 9, e53350 (2020).

    Article  PubMed  PubMed Central  Google Scholar 

  59. Tobin, W. F., Wilson, R. I. & Lee, W.-C. A. Wiring variations that enable and constrain neural computation in a sensory microcircuit. eLife 6, e24838 (2017).

    Article  PubMed  PubMed Central  Google Scholar 

Download references

Acknowledgements

This study benefited from the public release of the hemibrain connectome by the FlyEM Team at Janelia. We thank I. S. Haber and A. A. Li for tracing and annotation in the full adult female brain dataset (FAFB)25; N. Eckstein, A. S. Bates, J. Funke and G. X. E. Jefferis for neurotransmitter predictions based on those data; J. Omoto for assistance with behavioural experiments; W. B. Dickson for sharing modified FicTrac software and machining help; T. Wolff, G. M. Rubin, V. Jayaraman, G. Card, B. D. Pfeiffer, D. J. Anderson and H. Amrein for providing fly stocks; H. H. Yang, M. A. Basnak, M. J. Marquis, Y. E. Fisher, T. Okubo, A. Rayshubskiy, C. D. Harvey, B. L. de Bivort, J. Drugowitsch, B. el Jundi, C. Pehlevan, J. A. Assad and the Wilson laboratory for discussions. This work was supported by the Harvard Medical School Neurobiology Imaging Facility (NINDS P30 #NS072030), the HMS Research Computing Group O2 cluster, and the HMS Research Instrumentation Core Facility. This study was supported by NIH grants T32 GM007753, F30 DC017698 (to J.L.), R01 EB028171 (to S.D.), and U19 NS104655 (to M.H.D., S.D. and R.I.W.). R.I.W. and G.M. are HHMI Investigators.

Author information

Author notes

  1. These authors contributed equally: Amir H. Behbahani, Lydia Hamburg, Elena A. Westeinde

Authors and Affiliations

  1. Department of Neurobiology and Howard Hughes Medical Institute, Harvard Medical School, Boston, MA, USA

    Jenny Lu, Elena A. Westeinde, Paul M. Dawson & Rachel I. Wilson

  2. Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, CA, USA

    Amir H. Behbahani & Michael H. Dickinson

  3. Department of Neurobiology, Stanford University, Stanford, CA, USA

    Lydia Hamburg & Shaul Druckmann

  4. Laboratory of Integrative Brain Function and Howard Hughes Medical Institute, The Rockefeller University, New York, NY, USA

    Cheng Lyu & Gaby Maimon

Authors
  1. Jenny Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amir H. Behbahani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Lydia Hamburg
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Elena A. Westeinde
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Paul M. Dawson
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Cheng Lyu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Gaby Maimon
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Michael H. Dickinson
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Shaul Druckmann
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Rachel I. Wilson
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

J.L. and R.I.W. conceived the project and coordinated the work. J.L. designed and performed imaging experiments and analyses. A.H.B. and M.H.D. designed and performed behavioural experiments and analyses; M.H.D. also provided hardware and software support. L.H. and S.D. designed, implemented and analysed the computational model. E.A.W. designed and performed electrophysiological experiments and analyses. P.M.D. performed MCFO experiments. C.L. and G.M. provided the hΔB split-Gal4 line prior to publication. J.L. and R.I.W. analysed data and wrote the paper with input from all authors.

Corresponding author

Correspondence to Rachel I. Wilson.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks the anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Walking statistics on a spherical treadmill.

a. Distribution of forward × lateral, forward × rotational, and lateral × rotational velocities. Shown along each axis is the marginal distribution (gray lines on top right of each heatmap denote scale for the marginal distribution). Data are pooled across n=27 flies. We used the velocities recorded at the camera sampling rate (50 Hz) prior to down-sampling to volumetric calcium imaging rate. b. An example walking bout (30 s). Shown are the fly’s forward, lateral, and rotational velocity as well as its heading (based on the position of the visual cue shown in closed loop; note that we used a visual closed loop gain of 0.8×, meaning that the landmark is displaced by an azimuthal angle equal to 0.8× the ball’s yaw displacement). c. Fictive trajectory of the fly in 2D space based on the walking parameters in the example bout shown in b. The dotted line shows the calculated trajectory using only the forward velocity and the heading of the fly, ignoring the lateral velocity. The solid line shows the calculated trajectory using the forward velocity, lateral velocity, and heading of the fly. Note that the dotted line underestimates the curvature of the fly’s path.

Extended Data Fig. 2 PFNd tuning properties.

a. Circular correlation between bump and cue position for PFNd (n=16 flies) and EPG neurons (n=5 flies). Note that PFNd bump position is not as correlated with heading as EPG activity is. This is because PFNd neurons conjunctively encode velocity and heading, whereas EPG neurons encode only heading. For example, when the fly walks forward right, the PFNd bump on the left diminishes in amplitude, and vice versa. When the left and right bumps have different amplitudes, this diminishes the accuracy of our estimate of the bump position. Moreover, when the fly steps backward, both PFNd bumps diminish in amplitude, which again makes it difficult to accurately estimate bump position. b. Normalized PFNd PB bump amplitude versus forward velocity (left), and lateral velocity (right). Gray lines are individual flies and the black line is the mean across flies (n=16 flies). Data from the right and left PB are combined, and lateral velocity is computed in the ipsilateral direction (so that, for PFNd.L neurons, leftward lateral velocity is positive and rightward lateral velocity is negative). The red line shows the linear fit to the mean line, with the fitted equation below each plot. c. Computation of preferred translational direction angle using the linear regression slopes for forward and lateral velocity. We used the ratio of the slopes of the linear fits to lateral and forward velocity to calculate the angle of preferred translational direction. d. PFNd data from Fig. 1g, re-plotted in polar coordinates. Here, normalized bump amplitude is displayed as a function of body-centric translation direction and binned by speed. e. Normalized PFNd bump amplitude versus velocity in the preferred translational direction (vp). Data from the right and left PB are combined and binned by the fly’s velocity orthogonal to the preferred translational direction (see schematic at right). Shown is the mean across flies (n=16 flies). Note that a positive value in the orthogonal axis is in the ipsilateral direction. Whereas there is a significant effect of velocity in the preferred direction (2-way ANCOVA, P<10−10), there is no significant effect of velocity in the orthogonal direction (p=0.97). f. Normalized PFNd bump amplitude versus lateral velocity in the ipsilateral direction. Data from the right and left PB are combined, binned by ipsilateral rotational velocity, and averaged across flies (n=16 flies). Whereas there is a significant effect of lateral velocity (2-way ANCOVA, P<10−10), there is no significant effect of rotational velocity (p=0.59). This analysis shows that there is little or no systematic relationship between PFNd activity and rotational velocity once we account for the effect of lateral velocity. Note that, because rotational and lateral velocity are correlated, rotational velocity bins are asymmetrically populated. g. Circular correlation between bump and cue position for PFNd neurons when the fly walks in darkness (n=7 flies). h. Normalized bump amplitude versus lateral velocity in the ipsilateral direction, binned and color-coded by forward velocity, for PFNd neurons when the fly walks in darkness (n=7 flies). Lateral velocity is measured in the ipsilateral direction, and data from the right and left PB are combined and then averaged across flies. Both forward and lateral velocity have a significant effect (2-way ANCOVA, P<10−10 and P<10−5).

Extended Data Fig. 3 PFNv tuning properties.

a. Circular correlation between bump and cue position for EPG (n=5 flies, reproduced from Extended Data Fig. 2a) and PFNv neurons (n=11 flies). Note that PFNv bump position is not as correlated with heading as EPG activity is. This is because PFNv neurons conjunctively encode velocity and heading, whereas EPG neurons encode only heading. In particular, PFNv bump amplitude is generally quite low when the fly is walking forward. b. Normalized PFNv PB bump amplitude versus forward velocity (left), and lateral velocity (right). Gray lines correspond to individual flies and the black line corresponds to the mean across flies (n=11 flies). Data for the right and left PB are combined, and lateral velocity is computed in the ipsilateral direction. The blue line shows the linear fit to the mean line, with the fitted equation below each plot. c. Computation of preferred translational direction angle using the linear regression slopes for forward and lateral velocity. We used the ratio of the slopes of the linear fits to lateral and forward velocity to calculate the angle of preferred translational direction. d. PFNv data from Fig. 1g, re-plotted in polar coordinates. Here, normalized bump amplitude is displayed as a function of body-centric translation direction and binned by speed. e. Normalized PFNv bump amplitude versus velocity along the angle of preferred translational direction (vp). Data are combined between the right and left PB and binned by the velocity along the angle of translational movement orthogonal to the preferred direction (see schematic at right). Shown is the mean across flies (n=11 flies). The orthogonal directions for the right and left PFNv population are shown (right); note that a positive value in the orthogonal axis remains in the contralateral direction for the given right/left population. Whereas there is a significant effect of velocity in the preferred direction (2-way ANCOVA, P<10−10), there is no significant effect of velocity in the orthogonal direction (p=0.30). f. Normalized PFNv bump amplitude versus lateral velocity in the ipsilateral direction. Data for the right and left PB are combined, binned by the ipsilateral rotational velocity, and averaged across flies (n=11 flies). For this cell type, both lateral and rotational velocity have significant effects (2-way ANCOVA, P<10−10 and P<0.005). Note that, because rotational and lateral velocity is correlated, rotational velocity bins are asymmetrically populated. g. Circular correlation between bump and cue position for PFNv neurons when the fly walks in darkness (n=4 flies). h. Normalized bump amplitude versus lateral velocity in the ipsilateral direction, binned and color-coded by forward velocity, for PFNv neurons when the fly walks in darkness (n=4 flies). Lateral velocity is measured in the ipsilateral direction, and data from the right and left PB are combined and then averaged across flies. Both forward and lateral velocity have a significant effect (2-way ANCOVA, p<10−7 for each factor).

Extended Data Fig. 4 Interaction between heading and velocity tuning in PFNd neurons.

a. Firing rate versus vp for all PFNd recordings. Data are divided into bins based on the proximity of the fly’s heading to the neuron’s preferred heading. Three of these cells are shown in Fig. 2b. b. Linear fits for one example cell. c. Fitted slope values (reproduced from Fig. 2b) and y-intercept values for all cells (n=14 cells in 9 flies). Horizontal lines indicate mean values. For both parameters, there is a statistically significant effect of heading (2-way paired t-tests, Bonferroni-corrected p values). However, the effect of heading on the slope is relatively large and consistent, as compared to the effect on the y-intercept, which is smaller and less consistent. This implies that the effect of heading (θ) on the cell’s firing rate (f) is largely multiplicative, i.e., it controls the slope of the relationship between f and vp, as in f ∝ (cos(θ – θp) + a) vp + b where θp, a, and b are constants. In our computational model (Fig. 4a–d), we use this same relationship, with θp=0, a=1, b=0.

Extended Data Fig. 5 Connectomics analysis of inputs to PFNd and PFNv neurons.

a. Distribution of input synapses onto PFNd neurons from the hemibrain connectome24, grouped by cell type. Shown are the top ten cell type inputs onto PFNd neurons; all other identified cell types are grouped into “Other.” Collectively, the distribution shown comprises 94.2% of all input synapses onto PFNd neurons. Numbers indicate the percentage of synapses contributed by each input cell type. Note that Δ7 neurons and FB3A/4C/4M neurons are major inputs to PFNd neurons, but we did not screen these neurons as part of our search for the origin of body-centric velocity signals in PFNd neurons, for the following reasons: Δ7 neurons: Δ7 population activity is known to encode the fly’s heading direction, reflecting the strong input to Δ7 neurons from EPG neurons. It has been proposed that the function of Δ7 neurons is to reshape the heading bump into a cosine-shaped activity profile5,41. Thus, much of the “compass input” that we refer to in our study as originating from EPG neurons is probably due to the combined action of EPG neurons (which constitute the primary computational map of the compass system) and Δ7 neurons (which reshape and reinforce the compass system output). FB3A/4C/4M neurons: These neurons are FB tangential cells, meaning their axons run across the entire horizontal extent of the FB, perpendicular to PFNd dendrites5. Like other FB tangential cells, these neurons receive input from outside the central complex and they synapse onto a variety of cell types in the FB. There is evidence that FB tangential cells encode information about context, behavioral state, and internal physiological needs, including the need for sleep5. b. Input connectivity matrix for PFNd neurons, shown for the top ten input cell types. Connections comprising 3 or fewer synapses are not shown. Note that the cell types that provide major unilateral input to PFNd neurons are LNO2, IbSpsP, EPG, SpsP, and LNO1. c. Same as (a) but for PFNv neurons. Collectively, the distribution shown comprises 93.1% of all input synapses onto PFNv neurons.

Extended Data Fig. 6 LNO2 and hΔB split-Gal4 line characterization.

a. GFP expression driven by the LNO2 split-Gal4 line: +; Mi{Trojan-p65AD.2}VGlut[MI04979-Tp65AD.2]; P{VT008681-Gal4.DBD}attP2. Shown is a coronal projection of a confocal stack through the anterior half of the brain. GFP staining is shown in green, and neuropil staining (nc82) is shown in magenta. The scale bar is 50 µm. Note that, in addition to targeting LNO2 neurons in the LAL, there are some cells labeled in the superior brain which are not LNO2 cells. The observation that this VGlut-split-Gal4 construct drives expression in LNO2 neurons is evidence in support of the conclusion that LNO2 neurons are glutamatergic. b. Same as (a) but for individual optical slices. Shown are the location of the LNO2 cell bodies (left, arrows), neurites in the LAL (middle, arrows), and neurites in NO2 (right, arrows). Scale bars are 50 µm. c. Skeleton of LNO2 neuron from the hemibrain dataset. Overlaid are the anatomical boundaries of the LAL and the NO (divided into subunits NO1, NO2, and NO3). The black sphere denotes the position of the cell body. There is one LNO2 neuron per hemisphere. d. MCFO labeling of a single LNO2 neuron from the LNO2-split Gal4 line. Scale bar is 50 µm. e. On occasion, the LNO2 split-Gal4 line shows expression in NO3. Shown is an MCFO sample from the LNO2-split Gal4 line that labels this additional neuron in NO3 (arrow). Given that two channels (green and red) label the LNO2 on the ipsilateral side, whereas only one channel (red) shows the NO3-innervating neuron, this neuron appears to be a distinct neuron from LNO2. Scale bar is 50 µm. f. Skeletons of two hΔB neurons from the hembrain dataset. Overlaid are the anatomical boundaries of the FB. Spheres denote soma positions. g. MCFO labeling of two hΔB neurons from the hΔB split Gal4 line +; P{R72B05-p65.AD}attP40; P{VT055827-Gal4.DBD}attP2. Scale bar is 20 µm.

Extended Data Fig. 7 SpsP, LNO2, IbSpsP, and LNO1 physiology.

a. Schematic of SpsP and LNO2 input onto a single PFNd neuron. PFNd neurons have dendrites in the PB on the side ipsilateral to their soma, and dendrites in the NO on the side contralateral to their soma. As a result, PFNd neurons receive input from ipsilateral SpsP neurons and the contralateral LNO2 neuron. Thus, although SpsP and LNO2 neurons have opposite velocity preferences (Fig. 2c), they have congruent effects on PFNd neurons. b. SpsP and LNO2 activity as a fly walks in closed loop with a visual cue. c. SpsP and LNO2 ΔF/F versus lateral velocity in the ipsilateral direction. Data for the right and left PB are combined, binned by the ipsilateral rotational velocity, and averaged across flies (n=8 flies for SPS, 4 flies for LNO2). Because rotational and lateral velocity are correlated, rotational velocity bins are asymmetrically populated. There is a significant effect of lateral velocity (2-way ANCOVA, P<10−10 for both SpsP and LNO2) but not rotational velocity (p=0.59 for SpsP, p=0.14 for LNO2). Note however that SpsP activity increases when rotational speed is high, for both ipsi- and contralateral rotations. d. Control experiments for SpsP optogenetic activation. There is little effect of light in PFNd recordings from flies where an empty split-Gal4 line is combined with UAS-CsChrimson (n=3) or in flies with UAS-CsChrimson expressed under SpsP split-Gal4 control (ss52267) but reared in the absence of all-trans-retinal (ATR; n=3). We consistently see strong inhibition in flies that express UAS-CsChrimson under SpsP split-Gal4 control (ss52267) and that are raised on culture media containing ATR (n=9, reproduced from Fig. 2d). PFNd recordings were performed in TTX to isolate monosynaptic responses (see Methods). e. Each IbSpsP neuron receives input from the inferior bridge (IB) and SPS, and projects to a few adjacent PB glomeruli. f. Circular correlation between visual cue position and IbSpsP bump position (n=8 flies). Shown for comparison is the circular correlation for EPG neurons (n=5 flies), reproduced from Extended Data Fig. 2a. g. IbSpsP population activity in the PB as a fly walks in closed loop with a visual cue. h. Normalized IbSpsP bump amplitude versus forward velocity. Data are binned by lateral velocity in the ipsilateral direction, combined for the right and left PB, and averaged across flies (n=8 flies). There is a significant effect of lateral velocity (P<0.01) but not forward velocity (p=0.65, 2-way ANCOVA). i. Normalized IbSpsP bump amplitude in the PB, versus body-centric translational direction. Data are binned by speed. Lateral velocity is expressed in the direction ipsilateral to the imaged PB, allowing us to combine data from the right and left PB before averaging across flies (n=8 flies). j. Each LNO1 neuron receives input from the LAL and synapses onto PFNv and PFNd dendrites in the NO. k. LNO1 activity as a fly walks in closed loop with a visual cue. We used jGCaMP7s in these experiments (rather than jGCaMP7f) because LNO1 fluorescence was dim with jGCaMP7f. l. LNO1 activity versus forward velocity. Data for the left and right NO are combined, binned by lateral velocity in the ipsilateral direction, and averaged across flies (n=8 flies). LNO1 activity decreases slightly with ipsilateral backward movement. There is a significant effect of both forward velocity (P<10−10) and lateral velocity (P<0.01, 2-way ANCOVAs).

Extended Data Fig. 8 PFN→hΔB connectivity.

a. Schematized projections of the PFNd and PFNv populations, from the hemibrain connectome. Gray numbers denote PB glomeruli3. Note that the mapping from PB glomeruli to FB horizontal locations is the same for PFNd (red) and PFNv (blue). For each cell type, each half of the PB contains a complete heading map (black arrows) which is projected onto the full horizontal axis of the FB. b. Top: PFN→hΔB connection matrix from the hemibrain connectome, reproduced from Fig. 3g. Note that, for a given hΔB neuron, PFN projections from the left and right PB are horizontally shifted, corresponding to the morphologies in (a). Bottom: Permuted PFN→hΔB connection matrix. Here, the shifts between left and right PFN matrices are eliminated. We used this permuted connection matrix in Fig. 4d (“left-right shift eliminated”).

Extended Data Fig. 9 Model performance as a function of relative synaptic weight.

a. hΔB dendrites receive PFNd and PFNv inputs at their dendrites. By contrast, hΔB axon terminals receive PFNd inputs but no PFNv input. In the bar plot at right, each bar represents one hΔB neuron in the hemibrain connectome (n = 19 neurons). The computational model in Fig. 4a–d assigns an equal weight to all synapses, meaning that all connections are simply weighted by the number of synapses they contain, regardless of whether they are axo-dendritic or axo-axonic connections. b. To determine if the model might perform better if we treated these connections differently, we systematically varied the weight of PFN synapses onto hΔB dendrites versus axons, and we used the population vector average of hΔB activity to decode the fly’s simulated movement. Grayscale heatmap shows the error in translational direction encoding (left) and speed encoding (right), with lower values indicating more accurate encoding. Note that we obtain the best translation direction encoding if we apply equal weight to axo-dendritic or axo-axonic connections (as we do in Fig. 4a–d). Speed encoding improves if we minimize the weight at the synapses onto hΔB axons; this is because this reduces the contribution of PFNd inputs (relative to PFNv), and so it tends to reduce the disproportionate gain when the fly is walking in the preferred direction φp of the PFNd population (Fig. 4c). We do not know whether axo-dendritic and axo-axonic connections are actually weighted equally in the real network, but the fact that we observe good encoding of φ in the hΔB population (Fig. 4h) suggests that these connections carry similar weight, at least as measured with jGCaMP7f. c. We also systematically varied the weight of PFNd and PFNv synapses. We obtain the best translation direction encoding if we apply equal weight to PFNd and PFNv connections (as we do in Fig. 4a–d). Speed encoding improves if we reduce PFNd weights, again because this reduces the disproportionate gain when the fly is walking in the preferred direction φp of the PFNd population (Fig. 4c).

Extended Data Fig. 10 hΔB bump deviations.

a. hΔB ΔF/F in each FB column as a fly walks in closed loop with a visual cue. When the fly steps laterally (indicated by the arrowhead), the bump deviates from the cue. b. Histograms showing the difference between cue position and bump position, mean-centered in each experiment, and binned by translation direction; n=4 flies for hΔB, 16 flies for PFNd, and 11 flies for PFNv, # = relatively poor correlation between cue and bump; these experiments are omitted from panel c. At more lateral translation angles, the hΔB bump deviates away from where it would be when the fly is walking forward. c. Mean difference between cue position and bump position. Each set of connected symbols is one experiment. For hΔB neurons (n=4 flies), we found the shift was significant when comparing left translation-heading deviations to centered translation-heading deviations (P=0.0013, 2-sided paired-sample t-test with Bonferroni-corrected α = 0.0167, CI = [−0.460, −0.191] radians) and when comparing right translation-heading deviations to centered translation-heading deviations (P=0.0115, α = 0.0167, CI = [−0.698, −0.0473] radians). For PFNd neurons (n=16 flies), the shift is not significant when comparing left translation-heading deviations to centered translation-heading deviations (P=0.0215, 2-sided paired-sample t-test with Bonferroni-corrected α = 0.0167, CI = [−0.180, 0.0044] radians) or when comparing right translation-heading deviations to centered translation-heading deviations (P=0.4790, α = 0.0167, CI = [−0.0467, 0.0812] radians). For PFNv neurons (n=9 flies; 2 flies were excluded from our analysis), this shift is significant when comparing left translation-heading deviations to centered translation-heading deviations (P=0.0011, 2-sided paired-sample t-test with Bonferroni-corrected α = 0.0167, CI = [0.0544, 0.222] radians) but not significant when comparing right translation-heading deviations to centered translation-heading deviations (P=0.0313, α = 0.0167, CI = [−0.0135, 0.1848] radians); note that the shift is opposite to hΔB neurons. d. Same as Fig. 4f-g but color-coded by fly (n=28 epochs in 10 flies for hΔB, n=22 epochs in 6 flies for EPG). e. Maximum bump deviation versus φ, measured in all epochs ≥300ms when the φ was consistent over the epoch. Within each fly, epochs are binned by φ and then averaged (○) before averaging across flies (●). For hΔB neurons, the data are close to the identity line (purple); while for EPG neurons, the data are close to the zero line (gold). n=10 flies for hΔB, n=10 flies for EPG. f. Normalized hΔB bump amplitude versus φ, binned by speed (n=11 flies).

Supplementary information

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lu, J., Behbahani, A.H., Hamburg, L. et al. Transforming representations of movement from body- to world-centric space. Nature 601, 98–104 (2022). https://doi.org/10.1038/s41586-021-04191-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41586-021-04191-x

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing